Geodesic

Geodesic (pronounced jee-uh-des-ik or jee-uh-dee-sik)

(1) In spherical geometry, a segment of a great circle.

(2) In mathematics, a course allowing the parallel-transport of vectors along a course that causes tangent vectors to remain tangent vectors throughout that course (a straight curve, a line that is straight; the shortest line between two points on a specific surface).

1821: A back-formation from geodesy (surveying), the earlier forms being geodesical (1818) and, from the classical stem, geodetic (1819) (geodetical is from circa 1600). The geodesic dome, one built according to geodesic principles, is attested from 1953 and despite the earlier use in wartime aircraft construction, the use there was only ever casual.  The English use was influenced mostly the French géodésique, dating from 1815.  The alternative adjectival form geodetic is from 1834.

Four-dimensional space-time.

Geodesic describes the curve that locally minimizes the distance between two points on any mathematically defined space, such as a curved manifold; essentially the path is the one of the most minimal curvature so, in non-curved three-dimensional space, the geodesic is a straight line.  In General Relativity, the trajectory of a body with negligible mass on which only gravitational forces are acting (ie a free falling body), defines the geodesic in curved, four-dimensional space-time.

Sir Barnes Wallis (1887-1979) was an English engineer, best remembered as the inventor of the bouncing bomb used by the Royal Air Force in Operation Chastise (the Dambusters raid) to attack the Ruhr Valley dams during World War II and the big Tallboy (6 tonnes) and Grand Slam (10 tonnes) deep-penetration earthquake bombs.

Hull of Vickers R.100 Airship.

Wallis had been working on the Admiralty’s R.100 airship when he visited the Blackburn aircraft factory and was surprised to find the primitive wood-and-canvas methods of the Great War era still in use, a notable contrast to the elegant and lightweight aluminum structure of airships.  He was soon recruited by Vickers to apply his knowledge to the new generation of fixed-wing aircraft which would use light alloy construction for the internal structure.  His early experience wasn’t encouraging, the first prototype torpedo bomber, which used light alloy wing spars inspired by the girder structure of R.100, breaking up mid-air during a test-flight.  Returning to the drawing board, Wallis designed a revolutionary structural system; instead of using beams supporting an external aerodynamic skin, he made the structural members form the aerodynamic shape itself.

The geodesic structure in an airframe.

The principle was that the members followed geodesic curves in the surface, the shortest distance between two points in the curved surface although he only ever referred to it in passing as geodetic; it wouldn’t be until later the label came generally to be applied to the concept.  As a piece of engineering, it worked superbly well, having the curves form two helices at right angles to one another, the geodetic members became mutually supporting, rendering the overall framework immensely strong as well as comparatively light.  Revolutionary too was the space efficiency; because the geodetic structure was all in the outer part of the airframe meant that the centre was a large empty space, ready to take payload or fuel and the inherent strength was soon proven.  While conducting the usual wing-loading stress tests to determine the breakage point, the test routine was abandoned because the wings couldn’t be broken by the test rig.

Vickers Wellseley.

The benefits inherent in the concept were soon demonstrated.  Vickers’ first geodesic aircraft, the Wellesley, entered service in 1937 and in 1938, three of them, making use of the massive fuel capacity the structure made possible, flew non-stop from Ismailia in Egypt to Darwin in Australia, setting a new world record distance of 7,158 miles (11,265 km), an absolute record which stood until broken in 1946 by a Boeing B-29 Superfortress; it remains to this day the record for a single-engined aircraft with a piston engine, and also for aircraft flying in formation.  While the Wellesleys were under construction, Wallis designed a larger twin-engined geodetic bomber which became the Vickers Wellington, the mainstay of the RAF’s Bomber Command until 1943 when the new generation of four-engined heavy bombers began to be supplied in in the volume needed to form a strategic force.  Despite that, the Wellington was still used in many roles and remained in production until after the end of hostilities.  Over eleven-thousand were built and it was the only British bomber to be in continuous production throughout the war.

Vickers Wellington fuselage internal detail.

The final aircraft of the type, with a more complex geodetic structure was a four-engined heavy bomber called the Windsor but testing established it didn’t offer significantly better performance than the heavies already in service, and the difficulties which would be caused by trying to replicate the servicing and repair infrastructure was thought too onerous so it never entered production.  Post-war, higher speeds and operating altitudes with the consequent need for pressurised cabins rendered the fabric-covered geodetics obsolete.